Single crystal lithium niobate (LiNbO.sub.3) is a clear, colorless material having a reported melting point of 1,250.degree. C and a ferroelectric Curie point of 1,210.degree. C. It crystalizes in the trigonal system (3m) and single domain crystals of practical size can be grown by the Czochralski technique. The material has a high peizoelectric coupling coefficient, i.e., high electrical energy output to mechanical energy input, and vice-versa. These characteristics make single crystal lithium niobate useful in a variety of transducers in which the piezoelectric effect is important, such as in frequency determining elements, temperature measurement devices, and in accelerometers and other transducers utilizing mechanical force to generate a signal current. Some of the properties of lithium niobate have been discussed in the literature; see for example "Lithium Niobate: A High-Temperature Piezoelectric Transducer Material" by Fraser and Warner, Journal of Applied Physics, Vol. 37, No. 10, September 1966, pages 3853-3854, "Determination of Elastic and Piezoelectric Constants for Crystals In Class (3m)" by Warner, Onoe and Coquin, Journal of the Acoustical Society of America, Vol. 42, No. 6, 1967, pages 1223-1231, and "Piezoelectric and Elastic Properties of Lithium Niobate Single Crystals" by Yamada, Niizeki and Toyoda, "Japanese Journal of Applied Physics," Vol. 6, No. 2, February 1967, pages 151-155.
When utilizing such crystals for their piezoelectric effect, it is generally desired to measure sensitivity in only a single direction. This is particularly true with accelerometers used in measuring accelerations encountered in vibrations occurring in aircraft, missiles, and the like. However, piezoelectric crystals generally exhibit cross-axis sensitivity so that the signal resulting from the application of mechanical force does not accurately represent the amount of force exerted in a particular direction. As a result of this lack of unidirectional response, accelerometers are designed so that the mass exerting the force is constrained to apply force only along one measuring axis in relation to the crystal. A variety of mounting arrangements have been devised utilizing spring loading and the like in an attempt to reduce cross axis sensitivity. For example, in Tolliver et al. U.S. Pat. No. 3,233,465 an accelerometer is illustrated utilizing a piezoelectric crystal in a compressional mode of operation and the effect of cross axis forces are minimized by spring loading the inertial member against the crystal. In Shoor U.S. Pat. No. 3,104,335, an accelerometer is disclosed in which the piezoelectric crystal is mounted in shear relationship between the housing and the inertial member, and the device is designed to minimize cross-axis sensitivity by the provision of stress relief gaps. Other patents which disclose some form of compensation for unwanted crystal sensitivity include U.S. Pat. Nos. 3,060,333, 3,075,098, 3,075,099, 3,307,054, 3,349,259, 3,351,787 and 3,429,031. Other patents of interest herein with respect to piezoelectric crystal materials are U.S. Pat. Nos. 2,598,707, 2,714,672, 2,808,524, 2,864,713, 2,947,698, 2,976,246 and 3,471,721.
In accordance with the present invention, piezoelectric crystals are provided having low or zero cross axis sensitivity. In particular, lithium niobate single crystals are provided which have been cut from a larger crystal with certain selected orientations. For purposes of uniform reference in cutting the crystals, a Z axis has been chosen to coincide with the C (symmetry) axis of the crystal, an X axis has been chosen to lie in an a axis (mirror plane - perpendicular to the plane of symmetry) of the crystal and a Y axis has been chosen to lie perpendicular to the Z and X axes to give a conventional right handed rectangular coordinate system. For IRE notation, where the thickness dimension is along the Z axis, the X axis has been arbitrarily chosen as the length dimension; in all other cases, the Z axis has been arbitrarily chosen as the width dimension. Referring to such rectangular coordinate axes, in one form of the invention, lithium niobate single crystals are provided which can be utilized in a compressional mode transducer by orientating a crystal cut from a larger crystal along a plane (a) initially perpendicular to the Y axis and rotated 38.6 .+-.1.degree. counterclockwise around the X axis, in IRE notation an (yxl) +38.6.degree.(.+-.1.degree.) cut. In another form of the invention, lithium niobate single crystals can be provided for utilization in a shear mode transducer by orientating a crystal cut along a plane (a) initially perpendicular to the X axis and rotated about 31.7.degree. +1.degree. counterclockwise around the Y axis, in IRE notation a (zxtl) +60.degree.(.+-.1.degree.)/+51.4.degree.(.+-.1.degree.) cut or (b) initially perpendicular to the X axis and rotated 76.7.degree. .+-.1.degree. counterclockwise around the Y axis, in IRE notation an (xyl) +76.7.degree.(.+-.1.degree.) cut or symmetrical equivalents thereof. A symmetrical equivalent of the 38.6.degree. Y cut is obtained by cutting from a crystal along a plane initially perpendicular to the Z axis, rotated 60.0.degree. .+-.1.degree. counterclockwise around the Z axis to define an X' axis thereat and then rotated 51.4 .+-.1.degree. counterclockwise around the X' axis.